Metadatos del ítem

[EN] We study spaces X which have a countable outer base in βX; they are called ultracomplete in the most recent terminology. Ultracompleteness implies Cech-completeness and is implied by almost local compactness (≡having ...[+]

[EN] We study spaces X which have a countable outer base in βX; they are called ultracomplete in the most recent terminology. Ultracompleteness implies Cech-completeness and is implied by almost local compactness (≡having all points of non-local compactness inside a compact subset of countable outer character). It turns out that ultracompleteness coincides with almost local compactness in most important classes of isocompact spaces (i.e., in spaces in which every countably compact subspace is compact). We prove that if an isocompact space X is ω-monolithic then any ultracomplete subspace of X is almost locally compact. In particular, any ultracomplete subspace of a compact ω-monolithic space of countable tightness is almost locally compact. Another consequence of this result is that, for any space X such that vX is a Lindelöf Σ-space, a subspace of Cp(X) is ultracomplete if and only if it is almost locally compact. We show that it is consistent with ZFC that not all ultracomplete subspaces of hereditarily separable compact spaces are almost locally compact.[-]

[EN] The class of θ-compact spaces is introduced which properly contains the class of almost compact (generalized absolutely closed) spaces and is strictly contained in the class of quasicompact spaces. In the realm of ...

For a Tychonoff space X, we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a ...

[EN] A Tychonoff space X which satisfies the property that G(X) = C(Xδ) is called an RG-space, where G(X) is the minimal regular ring extension of C(X) inside F(X), the ring of all functions from X to R, and Xδ is the ...